CRYSTAL_ORIENTATION

Description

This class is used to load in particular crystal slip systems into gen_evp crystal potentials, or in separate crystal behaviors. The crystal orientation will define the number of slip systems in the model, as well as the number of independent interaction parameters between these slip systems.

The default orientations are as follows. For cubic crystals the (1 0 0)-axis is oriented horizontally to the right (along the zebulon \(x\)-axis), (0 1 0) vertically upwards (along the Zebulon \(y\)-axis) and (0 0 1) out of the paper towards the reader (along the Zebulon \(z\)-axis). For hexagonal crystals, the directions in the basal plane are depicted in the following figure (after [Tome and Kocks 1985]), and the \(c\)-axis coincides with the Z-set \(z\)-axis.

The crystal orientation will provide the localization tensors for the different slip systems \(i\) in a crystal:

\[\tau_i = \ten m_i:\ten \sigma\]

with \(\tau_i\) the resolved shear stress on slip system \(i\) and \(\ten \sigma\) the ’macroscopic’ stress tensor. For each slip system \(i\) in the particular crystal set, the second order Schmid tensor \(\bf m_i\) is defined as follows:

\[\ten m_i = \dfrac{1}{2}\left[ \vect{n}_i \otimes\vect{l}_i \right] ,\]

with \(\vect{n}_i\) the normal of slip plane \(i\), and \(\vect{l}_i\) the corresponding slip direction.

Syntax

<creating-command> type [ *interaction h-coefs ] [ *c_over_a ] c/a value

In absence of the *interaction command, only self-hardening is taken into account (i.e. h1=1. and the other coefficients are 0.). For some hexagonal crystals the ratio of the length of the \(c\)-axis to the length of the \(a\)-axis is needed.

The following crystal systems are available:

cubic

This orientation is for the 6 FCC cubic systems with up to 3 hardening coefficients.

( 0 0 1)[-1 1 0 ]
( 0 0 1)[ 1 1 0 ]
( 1 0 0)[ 0 1 1 ]
( 1 0 0)[ 0-1 1 ]
( 0 1 0)[-1 0 1 ]
( 0 1 0)[ 1 0 1 ]

octahedral

This type of crystal is used for the 12 FCC octahedral slip systems, with up to 6 hardening coefficients.

( 1  1  1 )[-1  0  1 ]
( 1  1  1 )[ 0 -1  1 ]
( 1  1  1 )[-1  1  0 ]
( 1 -1  1 )[-1  0  1 ]
( 1 -1  1 )[ 0  1  1 ]
( 1 -1  1 )[ 1  1  0 ]
(-1  1  1 )[ 0 -1  1 ]
(-1  1  1 )[ 1  1  0 ]
(-1  1  1 )[ 1  0  1 ]
( 1  1 -1 )[-1  1  0 ]
( 1  1 -1 )[ 1  0  1 ]
( 1  1 -1 )[ 0  1  1 ]

basal

3 HCP basal slip systems with 2 hardening coefficients.

( 1 -2  1  0 )[ 0  0  0  1 ]
( 2 -1 -1  0 )[ 0  0  0  1 ]
( 1  1 -2  0 )[ 0  0  0  1 ]

prismatic

3 HCP second-order prismatic systems with 2 hardening coefficients.

( 1  0 -1  0 )[ 1 -2  1  0 ]
( 0  1 -1  0 )[ 2 -1 -1  0 ]
(-1  1  0  0 )[ 1  1 -2  0 ]

pyramidal0

6 pyramidal systems - requires c_over_a to be entered.

( 1  0 -1  1 )[ 1 -2  1  0 ]
( 0  1 -1  1 )[ 2 -1 -1  0 ]
(-1  1  0  1 )[ 1  1 -2  0 ]
(-1  0  1  1 )[ 1 -2  1  0 ]
( 0 -1  1  1 )[ 2 -1 -1  0 ]
( 1 -1  0  1 )[ 1  1 -2  0 ]

pyramidal1

12 additional pyramidal systems - requires c_over_a to be entered.

( 1  0 -1  1 )[ 2 -1 -1 -3 ]
( 1  0 -1  1 )[ 1  1 -2 -3 ]
( 0  1 -1  1 )[ 1  1 -2 -3 ]
( 0  1 -1  1 )[-1  2 -1 -3 ]
(-1  1  0  1 )[-1  2 -1 -3 ]
(-1  1  0  1 )[-2  1  1 -3 ]
(-1  0  1  1 )[-2  1  1 -3 ]
(-1  0  1  1 )[-1 -1  2 -3 ]
( 0 -1  1  1 )[-1 -1  2 -3 ]
( 0 -1  1  1 )[ 1 -2  1 -3 ]
( 1 -1  0  1 )[ 1 -2  1 -3 ]
( 1 -1  0  1 )[ 2 -1 -1 -3 ]

pyramidalPi1

( 1  0 -1  1 )[ 1 -2  1  0 ]
( 0  1 -1  1 )[ 2 -1 -1  0 ]
(-1  1  0  1 )[ 1  1 -2  0 ]
(-1  0  1  1 )[ 1 -2  1  0 ]
( 0 -1  1  1 )[ 2 -1 -1  0 ]
( 1 -1  0  1 )[ 1  1 -2  0 ]

pyramidalPi2

(-1  2 -1  2 )[-1  2 -1 -3 ]
( 2 -1 -1  2 )[ 2 -1 -1 -3 ]
( 1  1 -2  2 )[ 1  1 -2 -3 ]
( 1 -2  1  2 )[ 1 -2  1 -3 ]
(-2  1  1  2 )[-2  1  1 -3 ]
(-1 -1  2  2 )[-1 -1  2 -3 ]

twinning

6 twinning systems in hexagonal crystals - requires c_over_a to be entered.

( 1  0 -1 -1 )[ 1  0 -1  2 ]
( 0  1 -1 -1 )[ 0  1 -1  2 ]
(-1  1  0 -1 )[-1  1  0  2 ]
(-1  0  1 -1 )[-1  0  1  2 ]
( 0 -1  1 -1 )[ 0 -1  1  2 ]
( 1 -1  0 -1 )[ 1 -1  0  2 ]

bcc112

12 additional slip systems for bcc crystals. These also apply to Shockley partial dislocations in fcc crystals.

( 2  1  1 )[-1  1  1 ]
( 1  2  1 )[ 1 -1  1 ]
( 1  1  2 )[ 1  1 -1 ]
(-2  1  1 )[ 1  1  1 ]
( 1 -2  1 )[ 1  1  1 ]
( 1  1 -2 )[ 1  1  1 ]
( 2 -1  1 )[ 1  1 -1 ]
( 1  2 -1 )[-1  1  1 ]
(-1  1  2 )[ 1 -1  1 ]
( 2  1 -1 )[ 1 -1  1 ]
(-1  2  1 )[ 1  1 -1 ]
(-1  2 -1 )[-1  1  1 ]

climb_cfc

4 climb directions on octahedral planes:

( 1  1  1 )[ 1  1  1 ]
( 1 -1  1 )[ 1 -1  1 ]
(-1  1  1 )[-1  1  1 ]
( 1  1 -1 )[ 1  1 -1 ]

climb_cubic

3 climb directions on cubic planes:

( 1  0  0 )[ 1  0  0 ]
( 0  1  0 )[ 0  1  0 ]
( 0  0  1 )[ 0  0  1 ]

climb_cubic1

The first of the cubic climb directions:

( 1  0  0 )[ 1  0  0 ]

climb_cubic2

The second of the cubic climb directions:

( 0  1  0 )[ 0  1  0 ]

climb_cubic3

The third of the cubic climb directions:

( 0  0  1 )[ 0  0  1 ]

plane

Enter in a single slip system. The first system in octahedral could be entered in as:

**potential plane ( 1.  1.  1. ) (-1. 0.  1. )